Impairment sensitive selection of constellation points for communication across a channel

ABSTRACT

An impairment compensation sequence for use in a communications system susceptible to one or more potential impairments each periodic in an integer number of symbols includes N phases, wherein N is selected such that each potential impairment, if present, is periodic therein, and a sequence of symbols, the sequence organized to place at least one instance of each symbol from a predetermined set of symbols in each phase to allow detection of the potential impairments in each of the N phases. The potential impairments may include robbed-bit signaling and padding. Using estimates prepared based on such an impairment compensation sequence, individual phase intervals may be grouped according to similarity of apparent aggregate effect of the impairments thereon without identification of individual impairments active in the particular phases. Constellation points may then be assigned based on group characteristics corresponding to phase intervals. In an exemplary realization, constellation points are assigned for each of 6 constellation indices based on amplitude estimates characteristic of the groups with which each of 4 corresponding phase intervals are associated.

This patent application claims benefit of U.S. Provisional ApplicationNo. 60/146,780, filed Jul. 31, 1999.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to data communications, and moreparticularly, to digital impairment learning for pulse-code modulation(PCM) modems used in transmission paths compatible with digitalmodulation.

2. Description of the Related Art

Much of the public switched telecommunications network (PSTN) isimplemented using digital data transport. Nonetheless, significantportions of the PSTN are still based on analog technology. For example,the “local loop” portion of PSTN that connects a telephone subscriber toa central office (CO) is typically an analog loop. Additionally, analogportions may exist at other points along a communications path, e.g., asan analog channel in an otherwise digital circuit.

To achieve high downstream data rates in the PSTN, the currentgeneration of 56 Kbps modems no longer treat the communications path asan analog channel. Instead, such modems assume that there is only one(1) analog portion in a downstream transmission path from a digitallyconnected server modem to a client modem connected to an analog localloop. This configuration is reasonable in areas where most InternetService Providers (ISPs) and business customers are digitally connectedto the network and allows data signaling rates of up to 56 Kbps in thedownstream transmission path.

Although a variety of similar designs are available, modems conformingto the ITU-T Recommendation V.90 are illustrative. See generally, ITU-TRecommendation V.90, A Digital Modem and Analogue Modem Pair for Use onthe Public Switched Telephone Network (PSTN) at Data Signalling Rates ofup to 56 000 Bit/S Downstream and up to 33 600 Bit/S Upstream (09/98)hereinafter referred to as “Recommendation V.90”), the entirety of whichis incorporated by reference herein. Recommendation V.90 defines amethod for signaling between a modem connected to an analog loop (theanalog modem) and a modem connected to the digital trunk (the digitalmodem). Modems in accordance with Recommendation V.90 take advantage ofthis particular arrangement to increase the data rate from the digitalmodem to the analog modem.

Earlier generations of modems, e.g., those conforming to ITU-TRecommendation V.34 and/or earlier standards, suffered from quantizationnoise introduced in the conversion of analog signals to digital, PulseCode Modulation (PCM) codewords for transmission in digital portions ofthe PSTN. Modem modems, including modems conforming to RecommendationV.90, avoid the effects of PCM quantization by using a form of amplitudemodulation that allows voltage amplitude levels to be chosen from thequantization levels of the PCM coder/decoder (codec) in the CO.Recommendation V.90 matches the quantization levels to potentiallyeliminate quantization noise entirely in a downstream path from a servermodem to a line interface. Thus, Recommendation V.90 achieves higherdata rates when there are no analog-to-digital conversions between aV.90 digital modem and the PSTN. A digital V.90 modem transmits PCMcodewords that are converted to discrete analog voltage levels in thelocal CO and are sent to the analog V.90 modem via the analog localloop. The analog modem's receiver then reconstructs the discrete networkPCM codewords from the analog signals received.

There is no specific technique provided in Recommendation V.90 by whichthe analog client modem is to decide whether PCM signaling can besupported by the downstream channel. Rather, the client modem must makean inference about the condition of the channel during the trainingprocess. Moreover, part of the modem training procedure, defined inRecommendation V.90, includes estimating the digital impairments presenton the telephone channel. Several common sources of digital impairmentsare Robbed Bit Signaling (RBS), transcoding (e.g., A-law to μ-lawconversion), and digital attenuation pad.

Using current techniques, 56 Kbps downstream signaling rates can oftenbe achieved. However, actual signaling rates may be limited bydistortion introduced in the digital backbone itself. One source ofdistortion is Robbed Bit Signaling (RBS). RBS is an in-band signalingtechnique used in some portions of the PSTN to perform control functionssuch as conveyance of ring and call progress indications in thetelephone network. In short, RBS involves modification by the PSTN ofdata transmitted. Generally, a least significant bit (LSB) of certainPCM codewords may be used (or usurped) by a portion of the digitalbackbone. Although usurpation of bits is generally acceptable whencodewords carry a voice signal, RBS effectively acts as noise ordistortion when codewords carry a data signal. Moreover, RBS limits theinformation carrying capacity of a communications channel that includesa portion employing it.

Recognizing these limitations, techniques have been developed fordetecting, characterizing and mitigating RBS. For example, U.S. Pat. No.5,875,229 to Eyuboglu et al., proposes detection and characterization ofRBS during a “training” phase prior to other training operations such asinitialization of equalizer coefficients. Eyuboglu's characterizationtechnique is based on counting LSB values equal to logic zero and logicone in each of 24 intervals of a received training signal. U.S. Pat. No.5,859,872 to Townshend also proposes a scheme for handling RBS in whichRBS is detected during an initial training phase. In Townshend, adecoder first attempts to equalize a received training signal having aknown pattern by minimizing the difference between its output and aknown pattern under the assumption that no robbing of bits occurred. Thedecoder then measures the average equalized values at each of six phasesand determines for each phase which of 4 bit robbing schemes (includingno bit robbing) has been employed. Once the bit robbing that occurred ineach phase is determined, the equalization process is rerun, since thefirst equalization was performed without knowledge of the bit robbing.

Recommendation V.90 specifies a protocol between digital and analog PCMmodems, whereby a Digital Impairment Learning (DIL) sequence is suppliedto allow the analog PCM modem to detect digital impairments in acommunication path. In this way, the analog PCM modem may define aconstellation (or constellations) that tend to avoid or compensate forthe discovered impairments. The protocol defined in Recommendation V.90allows each manufacturer to define a Digital Impairment Learning (DIL)sequence to meet its objectives.

SUMMARY OF THE INVENTION

Accordingly, a class of impairment compensation sequences and relatedtechniques have been developed. In some realizations, impairmentcompensation sequences are intended to be requested and supplied as aDIL sequence in accordance with the protocols of Recommendation V.90.However, other similar realizations, e.g., based on proprietary orfuture protocols, as well as realizations without a formal or genericrequest/response protocol, are also envisioned and will be appreciatedby persons of ordinary skill in the art based on the description herein.

In general, techniques in accordance with the present inventionemploying impairment compensation sequences accept the characteristicsof each timing phase as presented and need not make a priori assumptionsabout RBS or other digital impairments in the communication channel.Accordingly, the impairment compensation sequences and relatedtechniques are robust to digital impairments, including new digitalimpairments encountered in the field, that are periodic in N phases ofthe impairment compensation sequence as explained in greater detailherein. For example, in the case of RBS impairments, previous approacheshave required knowledge of the RBS forms present in the telephonenetwork. In contrast, 24-phase impairment compensation sequences inaccordance with some embodiments of the present invention areindifferent to the particular form of RBS present, including overlaidcontributions of various digital portions of a communications path, aslong as all RBS is periodic in the 24 phases. Indeed, usingcomplementary techniques described herein, impairment compensation maybe achieved without identification of the specific RBS forms affecting acommunications path.

Accordingly, realizations of communications apparatus and methodsemploying such impairment compensation sequences and/or relatedtechniques generally do not require updated software or hardware if andwhen new impairments are encountered in the field or when used in aparticular communication networks. For impairments periodic in apredetermined number of phases of an impairment compensation sequence(e.g., RBS-related impairments with periods of 6, 12, or 24 phases of aDIL sequence in accordance with the present invention), new types and/orcombinations of impairments may be tolerated and communicationsfacilities employing impairment compensation sequences and/or techniquesin accordance with the present invention may conveniently adapt thereto.

In one embodiment in accordance with the present invention, a method ofselecting points for inclusion in a multipoint constellation includesgrouping phase intervals based on similarity of aggregate impairmentexhibited therein, calculating a characteristic set of symbol estimatesfor each such group and assigning constellation points for aconstellation index based on one or more characteristic setscorresponding thereto. The characteristic sets include contributions ofsymbol estimates from phase intervals associated with one or more otherconstellation indices. In one variation, the assigning is performedcollectively for each of J distinct constellation indices and includes:selecting, for each such constellation index, successive candidate nextconstellation points that, based on symbol estimates for the one or morecharacteristic sets corresponding to the constellation index, satisfy adistance metric with respect to a last assigned constellation point forthe constellation index, and assigning successive lowest power ones ofthe candidate next constellation points to respective constellations.

In another embodiment in accordance with the present invention, a methodfor mapping constellation points to one or more constellations issuitable for use in a communications system for communicating via achannel susceptible to one or more potential impairments each periodicin an integer N samples of a received signal. The method includesreceiving a sequence of symbol estimates organized into N phases, wherea respective one or more of the phases correspond to each of Jconstellation indices. The method further includes grouping the N phasesinto a set of characteristic groups according to aggregate effects ofthe periodic impairments, if any, present in the N phases and without apriori identification of individual forms of the periodic impairmentspresent therein, and for each of the J constellation indices, selectingconstellation points based on the characteristic groups associated withthe one or more respective phases.

In yet another embodiment in accordance with the present invention, acommunication device suitable for communicating, using one or moreconstellations, via a channel susceptible to one or more potentialimpairments each periodic in an integer N samples of a received signal,includes a receive path and an impairment compensator. The receive pathis for receiving from the channel a sequence of symbols organized into Nphases intervals, wherein respective ones of the phase intervalscorrespond to constellation indices. The impairment compensator iscoupled into the receive path during a training mode to receive thesequence and group the N phases thereof into a set of characteristicgroups according to aggregate effects of the periodic impairments, ifany. The impairment compensator selects, for each of J constellationindices, constellation points based on the characteristic groupsassociated with the respective phase intervals corresponding thereto. Inone variation, the characteristic groups associated with respectivephase intervals corresponding to a particular constellation indexinclude contributions of symbol receptions in grouped phase intervalscorresponding to other constellation indices; such that selection ofconstellation points for the particular constellation index is improvedby symbol receptions from substantially all phase intervals exhibitingsimilar aggregate effects of the periodic impairments. In anothervariation, the communication device further includes a transmit path,wherein the impairment compensator is coupled to the transmit path tosupply an encoding of the selected constellation points to a remotecommunications device.

In still yet another embodiment in accordance with the presentinvention, an apparatus includes apparatus means for organizing areceived sequence of symbol estimates into N phases, means for groupingthe N phases into a set of characteristic groups according tocorrespondence of aggregate effects of periodic impairments, if any,present in the N phases, and means for selecting constellation pointsusing symbol estimates characteristic of the grouped phases.

In still yet another embodiment in accordance with the presentinvention, a computer program product includes instructions executableon at least one processor to at least partially implement acommunications device. The instructions include an impairmentcompensation subset thereof executable to group N phases of a symbolsequence received by the communications device into a set ofcharacteristic groups according to correspondence of aggregate effectsof periodic impairments, if any, present in the N phases, the impairmentcompensation subset of instructions selecting constellation points usingsymbol estimates characteristic of the grouped phases.

In some realizations, an impairment compensation sequence in accordancewith the present invention is requested by an analog PCM modem using aDIL descriptor and supplied by a digital PCM modem as a DIL sequence allin accordance with phase 3 of a start-up sequence for modems thatconform to ITU-T Recommendation V.90. However, the techniques describedherein are also applicable to other data communications configurationsand equipment. These and other suitable configurations will be betterappreciated by persons of ordinary skill in the art based on thespecification that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerousobjects, features, and advantages made apparent to those skilled in theart by referencing the accompanying drawings.

FIG. 1 is a generalized flow diagram illustrating a digital networkincluding a public switched telephone network (PSTN) that employsrobbed-bit signaling (RBS).

FIG. 2 illustrates a communications path for server and client modemsshowing a configuration in which RBS is present in a digital channel.

FIG. 3A is a diagram illustrating phases of a symbol sequence that maybe transmitted over a communications path in accordance with anembodiment of the present invention.

FIG. 3B is a diagram illustrating the organization of an illustrativeimpairment compensation sequence in accordance with the presentinvention as supplied as a DIL sequence using the DIL descriptor requestand DIL segment supply framework of Recommendation V.90.

FIG. 4 is a flow diagram illustrating a method for grouping phaseintervals according to similarity of aggregate impairments in accordancewith an embodiment of the present invention.

FIG. 5 is a flow diagram illustrating a method for assigningconstellation points in accordance with an embodiment of the presentinvention.

FIG. 6 depicts an exemplary V.90 modem realization in which DigitalImpairment Learning (DIL) techniques in accordance with the presentinvention may be employed.

FIG. 7 depicts an exemplary V.90 modem realization in which DigitalImpairment Learning (DIL) techniques in accordance with the presentinvention may be employed.

The use of the same reference symbols in different drawings indicatessimilar or identical items.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

Although not limited thereto, some aspects of the present invention aredescribed herein in the context of terminology, protocols, standards,facilities, encoding and modulation schemes, communication networksand/or interfaces typical of the Public Switched Telephone Network(PSTN). In particular, some aspects of the present invention areillustrated in the context of a digital Pulse Code Modulation (PCM)network, Robbed-Bit Signaling (RBS) typically employed in portions ofthe current PSTN, and modem realizations conforming to ITU-TRecommendation V.90 and related standards. Nonetheless, this context ismerely illustrative. Indeed, based on the description herein, persons ofordinary skill in the art will appreciate realizations in accordancewith the present invention suitable for other communication facilitiesand networks, including point-to-point circuits, private networks andcommunications channels generally susceptible to digital impairments.

Accordingly, and subject to the foregoing, the following nomenclature ispresented for clarity in the description of certain illustrativeembodiments particularly suitable in the context of a PSTN/V.90-orientedimplementation framework:

GLOSSARY OF TERMS

A_(i,k) estimate of the i^(th) amplitude at the k^(th) timing phaseA′_(i,k) an averaged version of A_(i,k) c index used to point to aUchord φ denotes the empty set γ_(i) i^(th) subset of Σ consisting ofall sets {σ_(j)} that exhibit the same or similar aggregate impairments(e.g., from one or more RBS forms active in corresponding time indices)Γ the set, {γ₀, γ₁, . . . , γ_(M−1)}, of subsets of Σ d(σ_(i),σ_(j)) sumof the amplitude differences-squared in the sets σ_(i) and σ_(j) (setdifference) DIL Digital Impairment Learning sequence d_(min) minimumdistance parameter H_(c) used to calculate the length of theDIL-segments containing training symbols from Uchord_(c). i arbitraryinteger index j arbitrary integer index k arbitrary integer index L_(c)length of one DIL-segment L_(SP) length of the sign pattern L_(TP)length of the training pattern l arbitrary integer index m arbitraryinteger index M the number of elements in Γ N number of DIL-segments rarbitrary integer index REF_(c) reference symbol in the DIL-segmentcontaining training symbols from Uchord_(c). PCM Pulse Code ModulationP_(max) maximum power transmitted by digital modem Ri reference symbolat time index i s_(m) number of elements in (i.e. the size of) the setγ_(m) SP sign pattern σ′_(i) a representative element of γ_(i) σ_(k) setof all estimated amplitudes at time index k Σ {σ_(k); k = 0, 1, . . . ,23} Ti training symbol at time index i TP training pattern θ thresholdless than which a set difference is defined to be small Ucode Auniversal code used to refer to a symbol value whether encoded as aμ-law or an A-law PCM code word. Uchord_(c) The c^(th) subset of Ucodes.Ucodes are grouped into eight Uchords. Uchord₁ contains Ucodes 0 to 15;Uchord₂ contains Ucodes 16 to 31; . . . ; and Uchord₈ contains Ucodes112 to 127. x(k) denotes equalizer input sample at time index k y(k)denotes equalizer output sample at time index kDigital Impairments (including RBS) in the PSTN

A conventional network is shown in FIG. 1. Network 100 includes adigital network such as public switched telephone network (PSTN) 100that includes a digital backbone 110. In the configuration shown, dataprocessing equipment 121, such as an internet server or gateway thereto,communicates with a digital adapter 123, such as a digital V.90 modem,during data communications with data processing equipment 122, e.g., auser's computer. Digital adapter 123 transmits a sequence of symbolsover digital backbone 110 to line interface 124. Line interface 124 inturn transmits baseband signals on local loop 126. Local loop 126typically transmits voice signals or binary data in the form of basebandsignals to analog adapter 125.

Analog adapter 125, e.g., an analog V.90 modem, receives the basebandsignals and may, in turn, equalize and sample the baseband signal,detect the binary information in the demodulated signal and supplyresults to data processing equipment 122. A reverse path from analogadapter 125 to digital adapter 123 may be constructed using conventionalanalog modem signaling techniques, such as, for example, V.34technology, or other suitable techniques. See generally, U.S. Pat. Nos.5,875,229 and 5,859,872; see also Recommendation V.90 for a descriptionof digital/analog modem pair technology.

Digital backbone 110 typically transmits encoded representations ofsymbol sequences. In an illustrative realization, symbols are encoded asA-law or μ-law pulse code modulation (PCM) codewords, each eight bits inlength. Line interface 124 receives the encoded symbols from digitalbackbone 110 and an A-law or μ-law decoder prepares the symbols fortransmission via local loop 126. In a typical realization, lineinterface 124 produces discrete baseband signals that correspond toinverse quantized symbols that are transmitted to analog adapter 125.Analog adapter 125 receives the baseband signals and obtains thetransmitted data through signal processing techniques. Data processingequipment 122, in turn, receives the transmitted data from analogadapter 125.

In an illustrative communications network, digital backbone 110 is partof a PSTN that either employs robbed bit signaling (RBS) or exhibitsother digital impairments. Such impairments typically introducedisturbances that have a very small effect on human perception of voicesignals, but effectively act as noise or distortion when codewordsencode data. Accordingly, digital impairments such as RBS limit theinformation carrying capacity of a communications channel. Focusing onan illustrative digital impairment, RBS is an in-band signalingtechnique used in some portions of the PSTN to perform control functionssuch as conveyance of ring and call progress indications in thetelephone network. In portions of the PSTN employing the technique, RBSmay result in modification of data transmitted. Generally, a leastsignificant bit (LSB) of certain PCM codewords may be used (or usurped)by a portion of the digital backbone.

FIG. 2 illustrates a downstream communications path in which RBS ispresent in a digital channel 216. Server modem 212, e.g., a digital V.90modem, generates a digital signal that forms an input to a decoder 217,e.g., an A-law or a μ-law decoder. At least some portion of digitalchannel 216 employs RBS, which “steals” certain low order bits ofcertain transmitted symbols to instead convey call progress or otherindications. Persons of ordinary skill in the art will appreciate thatindividual portions of the digital channel 216 may each employ RBSaffecting the same or different transmitted symbols, such that aconveyed sequence of symbols may be affected by multiple, possiblyoverlapping, RBS-type digital impairments. Decoder 217 converts thedigitally encoded signals received from modem 212 via digital channel216 and supplies a corresponding modulated analog signal via analogchannel 218. Analog channel 218 conveys the modulated analog signal toclient modem 219, e.g., an analog V.90 modem. Accordingly, the receivedsignal may be affected by multiple, possibly overlapping, RBS-typedigital impairments.

FIG. 3A illustrates a symbol sequence 300 such as that transmitted bydigital adapter 123 over digital backbone 110. Referring to FIGS. 2 and3 in combination, some symbols, namely those PCM codewords transmittedin an interval affected by RBS, may be modified by digital channel 216.Typical sources of RBS tends to affect every sixth PCM codeword and,depending on the form employed, may force least significant bits (LSBs)of affected codewords to logic 1, to logic 0, or to logic 1 in someintervals and logic 0 in others. See generally, U.S. Pat. Nos. 5,875,229and 5,859,872 for a discussion of RBS forms employed in the digitalPSTN. Although a most basic period for RBS is six intervals, it has beenobserved that RBS, if employed, may exhibit a period of six, twelve ortwenty-four. For example, an all-one RBS pattern will exhibit an RBSperiod of 6 phase intervals and an alternating zero-one pattern willexhibit an RBS period of 12. Other patterns, such as a patternconsisting of repetitions of 0 and an alternating 1/0 (e.g., 01000100 .. . ) will exhibit an RBS period of 24. See generally, TIA DraftStandard, TR30.3/00-05-0xx (DRAFT 15 PN3857), North American TelephoneNetwork Transmission Model for Evaluating Analog Client and DigitallyConnected Server Modems (May 2000) for a description of RBS patterns andrelated modem test procedures.

Therefore, for illustrative purposes, symbol sequence 300 can be viewedas exhibiting twenty-four timing phases, e.g., phase 1, phase 2, . . .phase 24. Of course, symbols transmitted in a given phase may beaffected by multiple digital impairments, including multiple forms orsources of RBS. For example, in a digital channel including at least twoportions, symbols transmitted in intervals corresponding to phase 2 (seeFIG. 3A) may be affected by overlapping RBS contributions (or otherdigital impairment contributions) from each of the portions.Alternatively, RBS contributions (or other digital impairmentcontributions) may affect different phases. Whatever the overlap andphasing characteristics of the impairments, the resulting effects areguaranteed to be periodic in 24 intervals.

DIL Sequence Framework

The Digital Impairment Learning (DIL) framework specified byRecommendation V.90 may be employed in some realizations to allow ananalog V.90 modem to request (and receive from a digital V.90 modem) animpairment compensation sequence in accordance with the presentinvention. In such realizations, the impairment compensation sequencecan be encoded as a DIL sequence. Accordingly, certain aspects of thepresent invention may be best understood when described in the contextof the DIL descriptor request/sequence supply protocol specified byRecommendation V.90. Nonetheless, based on the description herein,persons of ordinary skill in the art will appreciate realizations inwhich (1) an alternative descriptor request/sequence supply protocol isemployed or (2) no descriptor request/sequence supply protocol isemployed. In general, impairment compensation sequences in accordancewith the present invention may be requested, supplied, supplied withoutrequest, encoded, etc. in accordance with any suitable implementationframework. Subject to the forgoing, and without limitation, arealization particularly appropriate for the DIL framework ofRecommendation V.90 is now described.

To facilitate compensation for digital impairments such as RBS, modemdesigns in accordance with Recommendation V.90, implement a digitalimpairment learning protocol that supports a wide variety ofimplementations techniques (often vendor specific techniques) forascertaining, compensating and/or avoiding impairments present in agiven communications channel. In some embodiments, equalizer and echocancellation training (or retraining) at an analog V.90 modem mayexploit a digital impairment learning (DIL) sequence transmitted by thedigital V.90 modem. Typically, the DIL sequence is received andprocessed by the analog modem to determine the digital impairmentspresent in the connection, for example, the digital PAD value, the RBSpattern, and nonlinear distortion.

In an illustrative realization, an impairment compensation sequence inaccordance with the present invention is requested and supplied usingthe DIL framework of Recommendation V.90. Referring illustratively toFIG. 2, during a training phase of operation (e.g., phase 3 of thestartup sequence defined by Recommendation V.90), analog client modem219 requests a particular DIL sequence using a DIL sequence descriptor.The DIL sequence descriptor is sent from analog client modem 219 todigital modem 212. In response, digital modem 212 supplies acorresponding DIL via digital channel 216.

The specific requirements of Recommendation V.90 are well known (seegenerally, ITU-T Recommendation V.90, §§ 8.3, 9.3, which areincorporated herein by reference) and suitable implementations inaccordance therewith will be appreciated by persons of ordinary skill inthe art. However, to summarize operations in the context of FIG. 2,analog client modem 219 transmits a sequence requesting that digitalmodem 212 begin equalizer training. Analog client modem 219 thentransmits a training signal, TRN. After training its receiver, digitalmodem 212 receives a sequence, J_(a), from the analog client modem 219and subsequently transmits a training signal, TRN_(1d), for use byanalog client modem 219 in its equalizer and/or echo cancellationtraining. In an exemplary realization in accordance with RecommendationV.90, the sequence, J_(a), encodes a DIL descriptor. A suitable formatfor the DIL descriptor appears in ITU-T Recommendation V.90, § 8.3,Table 12, which is incorporated herein by reference. Digital modem 212and analog client modem 219 subsequently exchange sequences, J_(d) andJ_(d)′, and signals, S and S, whereupon digital modem 212 transmits aDIL sequence corresponding to the DIL descriptor.

DIL Sequence and Descriptor Formats

In some realizations in accordance with the present invention, animpairment compensation sequence is supplied as a DIL sequence andspecified using parameters of a DIL descriptor supplied (e.g., by analogmodem 219) in accordance with Recommendation V.90. In such realizations,the set of suitable impairment compensation sequences is constrained toa subset of all the possible sequences otherwise in accordance with thedescription and claims herein. In particular, the suitable subset isconstrained by the DIL sequence organization specified by RecommendationV.90 and by the limited expressiveness of the DIL descriptor requestformat specified in Recommendation V.90. Persons of ordinary skill inthe art will appreciate nature of these Recommendation V.90-relatedconstraints based on the following description.

According to Recommendation V.90, a DIL sequence consists of NDIL-segments of length L_(c) where:

0≦N≦255;

1≦c≦8; and

L_(c)=(H_(c)+1)*6 symbols.

In the DIL scheme of Recommendation V.90, N, a set of N trainingsymbols, a set of reference symbols, segment lengths, and a pattern oftraining and reference symbols (including a sign pattern) are allspecified as part of the DIL descriptor.

In particular, each DIL segment in accordance with Recommendation V.90includes a single training symbol (e.g., a Ucode) from the set specifiedin the DIL descriptor. Both a segment length and a reference symbolvalue may be individually specified for the set of Ucodes (and DILsegments) corresponding to a particular Uchord. For example, each H_(c)specifies the length of the DIL-segments containing training symbolsfrom the corresponding Uchord_(c). Similarly, each REF_(c), specifiesthe reference symbol for use in DIL-segments containing training symbolsfrom the corresponding Uchord_(c). A sign pattern (SP) and trainingpattern (TP) are used for the entire DIL sequence. The pattern of SPbits determines the pattern of sign for symbols of the DIL sequence.More particularly, values of 0 and 1 indicate negative and positiveUcode signs, respectively. Similarly, the pattern of TP bits determinesthe pattern of reference and training symbols in the DIL sequence. Moreparticularly, values of 0 and 1 indicate a reference symbol (REF_(c))and training symbol, respectively. Patterns are restarted at thebeginning of each DIL-segment. The lengths of these patterns are:

1≦L_(SP)≦128; and

1≦L_(TP)≦128.

Based on the description herein, DIL-descriptor formats andcorresponding DIL sequences will be readily understood by persons ofordinary skill in the art familiar with Recommendation V.90.Accordingly, DIL-descriptors may be used to specify DIL sequencerealizations of impairment compensation sequences in accordance with theclaims that follow and provide a useful framework for description.Nonetheless, DIL sequence realizations are merely exemplary andimpairment compensation sequences in accordance with the presentinvention need not comport with Recommendation V.90 or with a descriptorrequest/sequence supply protocol.Impairment Compensation Sequences

In an exemplary embodiment in accordance with the present invention, animpairment compensation sequence may be employed to conform acommunications device to at least a subset of impairments that may bepresent in a communications channel. For example, estimates (e.g.,amplitude estimates) corresponding to training symbols (e.g., PCM codewords) may be computed and adaptive signal processing structures (suchas equalizers, echo cancellers, etc.) may be trained using a receivedimpairment compensation sequence transmitted over the affectedcommunications channel. In addition, symbol sets may be selected basedon the characteristics of the received impairment compensation sequence.

In accordance with the present invention, an exemplary DIL-sequencedescribed herein is designed in order to estimate the receivedamplitudes associated with all possible ucodes that could be transmittedby the remote modem. Further, the received amplitudes are observed ateach of 24 possible time phases. The period of 24 is chosen to coincidewith all possible periods of RBS sequences that might be employed on thedigital channel. Actual RBS sequences have unknown periods of either 6,12, or 24, so observing the received amplitudes at 24 distinct timephases subsumes all cases.

In particular realizations in accordance with the present invention,impairments that are periodic in N phases of a signal conveyed by thecommunications channel are addressed using impairment compensationsequences wherein at least one instance of each symbol is placed in eachof the N phases thereof. An illustrative periodic impairment is RBS,which, in current communication systems, is periodic in 6, 12 or 24symbol intervals of the PSTN. Accordingly, in an RBS-orientedembodiment, an impairment compensation sequence preferably presents eachsymbol that is, or may be, employed in communication via the affectedcommunications channel in each of 24 phases of the impairmentcompensation sequence. In this way, estimates may be calculated for eachsymbol in each phase that may be affected by one or more RBS-typeimpairments. Since actual RBS impairments have periods that are notknown a priori, but which must be 6, 12, or 24 symbol intervals,estimating corresponding amplitudes at each of 24 phases subsumes allcases.

In general, an impairment compensation sequence in accordance with thepresent invention includes N phases, wherein N is selected such thateach potential impairment, if present, is periodic therein. According toan exemplary embodiment, N is 24, as in the maximum period for RBS. Theimpairment sequence is a sequence of symbols organized to place at leastone instance of each symbol from a predetermined set of symbols in eachtime phase to allow detection of the potential impairments, such as RBSor PAD distortion, in each of the N phases. Another quality of theimpairment compensation sequence is that N is chosen to be a leastcommon multiple of respective periods of each of the potentialimpairments. Thus, the impairment compensation sequence establishescommunication avoiding impairments that have any integer multiple, andis not limited to RBS and PAD-type periodic impairments.

Suitable realizations of such impairment compensation sequences are, ingeneral, shaped by the characteristics of receiver signal processingstructures and by limitations of (or constraints imposed by) anydescriptor request/sequence supply protocol employed. For example, in areceiver that employs a particular equalizer design, e.g., a partialresponse, class five (PRV) equalizer, the organization of a suitableimpairment compensation sequence typically allows individual trainingsymbols to be isolated in equalizer output sequence. Similarly, in adescriptor request/sequence supply protocol (such as the DIL descriptorrequest/sequence supply protocol of Recommendation V.90) wherein aportions (e.g., segments) thereof each present a single training symbol,the organization of a suitable impairment compensation sequencetypically presents at least one instance of a first training symbol(typically interspersed with reference symbols), then at least oneinstance of a second training symbol, then . . . , in each of the Nphases of the impairment compensation sequence. In general, to improvethe quality of estimation of symbols received, the impairmentcompensation sequence is organized to place at least two instances ofeach symbol from a predetermined set of symbols in each phase. The twoor more instances can then provide an average of received valuescorresponding to the symbol.

Exemplary DIL Sequences

Based on the description and claims herein, persons of ordinary skill inthe art will appreciate the general characteristics of impairmentcompensation sequences in accordance with the present invention in thecontext of a particular realization thereof. Accordingly, an impairmentcompensation sequence is now described which is embodied as an exemplaryDIL sequence of symbols selected from the set of Ucodes employed in thePSTN, which is suitable for supply in response to a startup sequence inaccordance with Recommendation V.90 and its descriptor request/sequencesupply protocol, and which is particularly adapted for amplitudeestimation at a communications device (e.g., an analog V.90 modem)implementation employing a PRV or partial-response, class four (PRIV)equalizer. While the exemplary DIL sequence is particularly suited tosuch a configuration, persons of ordinary skill in art will understand,based on the more general description herein, that the invention is notlimited thereto.

Referring to FIG. 3B and Table 1 below, a first portion 351 (104symbols) of a DIL segment 350 of an exemplary DIL sequence 340 isillustrated. The complete DIL sequence is typically supplied in responseto a DIL descriptor (e.g., DIL descriptor 330) that specifies thecharacteristics of the desired DIL sequence. Column 1 of the tableindicates a time index k where a symbol is supplied at each timek={0,1,2, . . . 104, . . . }, while column 2 identifies each of 24phases. For each time index, a symbol (e.g., a reference or trainingsymbol) is supplied via a digital transport in which zero or more phasesmay be affected by zero or more RBS-type impairments. Each such symbolis received as a corresponding amplitude, x(k), which is supplied as aninput to an equalizer of the receiver (e.g., a PRV or PRIV equalizer ofa analog V.90 modem implementation). In the table, R representsinstances a reference symbol and T represents a training symbol.

TABLE 1 DIL-Sequence Equalizer Output [αy(k)] k Phase x(k) PR V PR IV 00 R — — 1 1 −R  — — 2 2 T — — 3 3 −T  — — 4 4 −R  T T 5 5 R −T  −T  6 6−T  — — 7 7 T — — 8 8 R −T  −T  9 9 −R  T T 10 10 T — — 11 11 −T  — — 1212 −R  T T 13 13 R −T  −T  14 14 −T  — — 15 15 T — — 16 16 R −T  −T  1717 −R  T T 18 18 T — — 19 19 −T  — — 20 20 −R  T T 21 21 R −T  −T  22 22−T  — — 23 23 T — — 24 0 R −T  −T  25 1 −R  T T 26 2 R — — 27 3 −R  — —28 4 −T  — — 29 5 T — — 30 6 −R  −T  −T  31 7 R T T 32 8 T — — 33 9 −T — — 34 10 R T T 35 11 −R  −T  −T  36 12 −T  — — 37 13 T — — 38 14 −R −T  −T  39 15 R T T 40 16 T — — 41 17 −T  — — 42 18 R T T 43 19 −R  −T −T  44 20 −T  — — 45 21 T — — 46 22 −R  −T  −T  47 23 R T T 48 0 T — —49 1 −T  — — 50 2 R T T 51 3 −R  −T  −T  52 4 R — — 53 5 −R  — — 54 6 T— — 55 7 −T  — — 56 8 −R  T T 57 9 R −T  −T  58 10 −T  — — 59 11 T — —60 12 R −T  −T  61 13 −R  T T 62 14 T — — 63 15 −T  — — 64 16 −R  T T 6517 R −T  −T  66 18 −T  — — 67 19 T — — 68 20 R −T  −T  69 21 −R  T T 7022 T — — 71 23 −T  — — 72 0 −R  T T 73 1 R −T  −T  74 2 −T  — — 75 3 T —— 76 4 R −T  −T  77 5 −R  T T 78 6 R — — 79 7 −R  — — 80 8 −T  — — 81 9T — — 82 10 −R  −T  −T  83 11 R T T 84 12 T — — 85 13 −T  — — 86 14 R TT 87 15 −R  −T  −T  88 16 −T  — — 89 17 T — — 90 18 −R  −T  −T  91 19 RT T 92 20 T — — 93 21 −T  — — 94 22 R T T 95 23 −R  −T  −T  96 0 −T  — —97 1 T — — 98 2 −R  −T  −T  99 3 R T T 100 4 T — — 101 5 −T  — — 102 6 RT T 103 7 −R  −T  −T  . . . . . . . . . . . . . . .

A first portion of a DIL segment is illustrated in column 3 of thetable. In particular, the organization of the first 104 symbols of anexemplary DIL segment is illustrated as a sequence of training andreference symbols. Corresponding amplitudes, x(k), are supplied as aninput to an equalizer of the receiver. Column 4 illustrates idealizedscaled outputs of a receiver employing a PRV equalizer wherein an outputtime sequence y(k) is related to the input time sequence x(k) by therelationship:y(k)=x(k)−2x(k−2)+x(k−4).Similarly, column 5 illustrates idealized scaled outputs of a receiveremploying a PRIV equalizer wherein an output time sequence y(k) isrelated to the input time sequence x(k) by the relationship:y(k)=x(k)−x(k−2).In each case, interesting outputs, i.e., those that are a function of asingle training symbol instance, are listed. Other outputs, indicated as“- - -” may be ignored. Note that in the case of outputs for the PR IVequalizer, only a single output based on each training symbol areillustrated. Duplicative outputs are ignored and the illustrated outputis selected for correspondence with PRV outputs although otherselections could also be made.

Inspection of the set of interesting equalizer outputs in Table 1confirms that a training symbol appears once with a positive sign andonce with a negative sign in each of the 24 possible time phases of theillustrated portion of a DIL segment. Each of these appearancescorresponds to an estimate of the amplitude level of the training symbolwhen observed at the receiver. In an exemplary realization, a completeDIL segment (e.g., DIL segment 350) includes two repetitions (351 and352) of the partial sequence illustrated in table 1 and therefore yieldstwo such estimates, thereby reducing the error associated with eachestimate by 3 dB, assuming that the errors are uncorrelated. In anexemplary realization, DIL sequence (e.g., DIL sequence 340) includes128 similarly organized DIL segments, one for each possible (positive)Ucode employed in the PSTN (see Table 1/Recommendation V.90). Inrealizations in accordance with Recommendation V.90, each DIL segmentpresents a particular Ucode as the training symbol T.

Accordingly, a DIL sequence employing 128 such DIL segments presentseach symbol (i.e., A_(i){i=−127,−126, . . . ,−1,−0,0,1, . . . ,127}) ineach of the 24 possible time phases of the DIL sequence. Such a DILsequence therefore provides 128 (Ucodes)×2 (positive and negative)×24(timing phases)=6144 estimates, each of which includes the average oftwo observations of each of 256 amplitudes at each of the 24 timingphases. In the description that follows, an estimate of the i^(th)amplitude at the k^(th) timing phase is denoted by A_(i,k) fori=−127,−126, . . . ,−1,−0,0,1, . . . ,127 and k=0,1, . . . ,23. (Notethat the elements A_(−0,k) and A_(0,k) are different in general.)

Exemplary DIL Descriptors

Although persons of ordinary skill in the art will appreciate a varietyof impairment compensation sequences in accordance with the presentinvention, including sequences supplied without use of descriptorrequest/sequence supply protocols or using alternate protocols,realizations in accordance with the particular descriptorrequest/sequence supply protocols of Recommendation V.90 areillustrative.

As discussed above, an impairment compensation sequence that is a DILsequence of reference (R) and training (T) symbols in accordance withRecommendation V.90, can be specified according to a logical combinationof sign pattern bits (SP) and training pattern bits (TP). Morespecifically, a server modem responding in accordance RecommendationV.90 supplies reference and training symbols according to the signpattern and the training pattern specified by a DIL descriptor.Typically, the particular symbol (reference or training) supplied atindex j of a DIL segment is a function of corresponding SP and TP bitvalues:

R if SP_(m)=1 and TP_(n)=0;

−R if SP_(m)=0 and TP_(n)=0;

T if SP_(m)=1 and TP_(n)=1; and

−T if SP_(m)=0 and TP_(n)=1

where j=0, . . . , L_(c)−1; m=j mod L_(SP); and n=j mod L_(TP). In thecontext of realizations in accordance with Recommendation V.90, a singletraining amplitude is supplied with positive and negative sign in thespecified positions of a particular DIL segment. At least one DILsegment is requested for each training Ucode. Corresponding referencesymbols for a group or Uchord of symbols are specified in accordancewith the Recommendation V.90-style DIL descriptor format.

Accordingly, in a realization employing a Recommendation V.90-style DILdescriptor to request a DIL sequence of 128 DIL segments, each asillustrated above with reference to Table 1 and respectivelycorresponding to one of the 128 PCM encoded Ucodes employed in thedigital PSTN, a suitable DIL descriptor encodes the following:

X=128;

L_(SP)=52; L_(TP)26;

SP={0xA5, 0xA5, 0xA5, 0xA5, 0xA5, 0xA5, 0x05};

TP {0xCC, 0xCC, 0xCC, 0x00};

L_(C)=210; H_(C)=34; and

REF_(C)=0; c=1,2, . . . 8.

The DIL segment length, L_(c), is specified as 210, which includes two104 symbol iterations of the partial DIL segment illustrated in Table 1with an extra two bits of padding to provide a DIL segment length,L_(c), that is a multiple of six. Sign pattern length, L_(SP), andtraining pattern length, L_(TP), are each selected to repeat evenlywithin the 208 symbol positions (210 less padding) of the DIL segmentand provide two (2) positive sign instances and two (2) negative signinstances of a particular training Ucode in each of the 24 phases of theDIL segment.

While a complete set of available symbols may be employed in somerealizations, a subset may be selected in accordance with powerconstraints of the system. More specifically, a specification such asRecommendation V.90, typically contemplates a limit to the amount ofpower transmitted across a communication channel. The PCM codewordincludes Uchords that transmit at different power levels. Therefore, theset of symbols employed for communication (and included in a DILsequence), may preferably be chosen to convey as much information aspossible within power constraints. In another realization, the DILsequence employs 112, rather than 128, Ucodes.

Determination of Characteristic Groups

Based on a received sequence such as the exemplary DIL-sequencesdescribed above, a communications device operating in accordance withsome embodiments of the present invention groups phases accordingcorrespondence of respective estimates. For example, in somerealizations, phases may be grouped by calculating a distance measurebetween phase-specific amplitude estimates of representative sets ofsymbols. An illustrative set difference calculation is described ingreater detail below. Because the exemplary sequences described aboveguarantee that individual symbols of a predetermined set appear at leastonce in each phase, such difference measure calculations arefacilitated.

Using distance measure calculations or other correspondence measurementtechniques, phases affected by the same or like impairments can beidentified and appropriate compensation can be applied to the group. Itis notable that a receiver employing techniques such as described hereinmakes few a priori assumptions about the communications channel. Forexample, the receiver of an analog client modem employing suchtechniques (see e.g., FIG. 2 in which analog client modem 219 receivesan impairment compensation sequence from digital server modem 212) neednot make assumptions about which timing phases are perturbed byparticular forms of RBS, padding or other artifacts of a digitalcommunications channel. Instead, such techniques exploit the fact thatthe disturbance(s), if any, introduced by the digital network isperiodic in a predetermined number of phases (typically 24). Thisassumption includes the common cases in which an RBS pattern exhibits aperiod of 6 or 12.

In the general case, each of the 24 phase intervals (see e.g., FIG. 3A)may, in theory, be affected by a different impairment or superimposedcollection of impairments. Alternatively, each of the 24 phase intervalsmay be affected by a single impairment (or superimposed collection ofimpairments) or no impairment at all. Focusing illustratively on RBSimpairments, presence of one or two distinct forms of RBS is common withless than all of the phase intervals affected. In general, the forms ofRBS that may affect a phase interval result in: (1) forcing a leastsignificant bit (LSB) of an octet to one; (2) forcing the LSB of anoctet to zero; and (3) forcing the LSB of an octet to a “randomly”selected value, either a zero or a one. Note that selection of a zero orone is only “random” with respect to the symbols conveyed over thecommunications channel. Selection is, of course, deterministic from thepoint of view of the in-band signaling that employs it.

For simplicity, much of the art assumes that a given phase interval isaffected by a single form of RBS, rather than a superposition ofmultiple forms. Similarly, it is often assumed that the single form ofRBS affecting a particular sample is periodic in 6 phase intervals.Strictly speaking, neither simplification is necessarily valid. Instead,persons of ordinary skill in the art will recognize that individualportions of a communication channel may employ differing forms of RBS invarious phase intervals. Accordingly, symbols conveyed over acommunication channel in a given phase interval may be affected bymultiple RBS forms or other impairments. Furthermore, as describedabove, the effects of RBS impairments may have periodicity of 12 or 24phase intervals. Embodiments in accordance with the present inventionmay be particularly advantageous in that diagnosis of a particular RBSor other impairment is unnecessary. Whatever the particular forms of RBSactive in a communications channel, realizations of the presentinvention may avoid diagnosis of the particular form(s) of RBS presentin an individual phase interval by instead categorizing the phaseintervals into characteristic groups according to the similarity ofobserved impairments.

Of course, in addition to RBS, other sources of impairments (such asdigital attenuation padding) may also affect some or all of the phaseintervals. Based on the description herein, persons of ordinary skill inthe art will appreciate a wide variety of potential impairments andcombinations of impairments that may affect the various phase intervals.Nonetheless, for clarity and without loss of generality, the descriptionthat follows focuses on RBS as the illustrative impairment.

Let the amplitude estimate for the i^(th) symbol of a predeterminedalphabet at the k^(th) timing phase be denoted by A_(i,k) fori=−127,−126, . . . ,−1,−0,0,1, . . . ,127 and k=0,1, . . . ,23. (Notethat, in general, the elements A^(−0,k) and A_(0,k) stand for differentestimates.) Further, define the sets σ_(k)={A_(i,k); −127≦i≦127} fork=0,1, . . . ,23. That is, σ_(k) is the set of all amplitude estimatesmade at timing phase k. Finally, define Σ={σ₀,σ₁, . . . ,σ₂₃}.

Based on the above, an illustrative set difference between σ_(i) andσ_(j), both elements of Σ, can be defined as:

${d\left( {\sigma_{i},\sigma_{j}} \right)} = {{\sum\limits_{l = {- 79}}^{- 48}\;\left( {A_{l,i} - A_{l,j}} \right)^{2\;}} + {\sum\limits_{l = 48}^{79}\;\left( {A_{l,i} - A_{l,j}} \right)^{2}}}$where the range of index values l for the summation operators covers arepresentative subset of amplitude estimates (e.g., amplitude estimatesfor PCM code words corresponding to Uchord₄ and Uchord₅ as employed inmodem communications in accordance with Table 1 of Recommendation V.90).Of course, the particular subset is merely illustrative and persons ofordinary skill in the art will recognize that any representative subsetof transmitted symbols (including all the transmitted symbols) may beemployed. Typically, impairment compensation sequences andconstellations employed for data communication do not employ a completeset of symbols (e.g., all 256 signed Ucodes) based on powerconsiderations.

Note that the above sum-of-squares set difference calculation is merelyillustrative, and any of a variety of measures for establishingcorrespondence between phase-specific sets of estimates is suitable. Forany suitable difference measure, a threshold or similar technique may beemployed to discriminate between phases to be attributed to the same ordifferent characteristic groups.

Based on the above, it is possible to define various subsets of Σ,Γ={γ₀,γ₁, . . . , γ_(M−1)}, with the properties that

${\bigcup\limits_{i = 0}^{M - 1}\gamma_{i}} = \;\sum$and γ_(i)ωγ_(j)=φ, i≠j, where φ denotes the empty set. That is, γ_(m)includes the set of amplitude estimates corresponding to phase intervalsthat can be associated with an m^(th) characteristic group, where m=0,1,. . . M−1 and 1≦M≦24. Define s_(m) to be the number of elements ofγ_(m). In general, a value of M=24 corresponding to 24 characteristicgroups each with a single corresponding phase interval (s_(m)=1) mayarise if each phase interval exhibits dissimilar impairmentcharacteristics (e.g., 24 distinct RBS forms). More typically, a valuesuch as M=3 may arise if the 24 phase intervals can be associated with 3dissimilar sets of impairment characteristics (e.g., 3 distinct RBSforms, including no RBS) wherein

${\sum\limits_{m = 0}^{2}\; s_{m}} = 24.$To facilitate grouping of phase intervals into characteristic groups, itis possible, for each γ_(m), to choose a representative set of amplitudeestimates, σ′_(m), such that σ′_(m)εΣ, σ′_(m)εγ_(m) and σ′_(i)∉γ_(m) ifi≠m. In general, σ′_(m) is any set of amplitude estimates that isrepresentative of the m^(th) characteristic group. In some realizations,σ′_(m) is a composite (or average) of estimates from the various phaseintervals that have been associated with the m^(th) characteristicgroup.

Based on the above definitions, the following pseudocode illustrates asequence of operations that may be implemented in a communication device(e.g., in software or firmware) for defining a set of characteristicgroups and associating individual phase intervals with thecharacteristic groups.

Initial step: M=1 γ₀={σ₀} σ′₀=σ₀ s₀=1 General step: for k=1 to 23 {found = false for m=0 to M−1 { if (d(σ′_(m),σ_(k))< θ) {γ_(m)=γ_(m)∪{σ_(k)} s_(m)=s_(m)+1 found = true break } } if !found {M=M+1 γ_(M−1)={σ_(k)} σ′_(M−1)=σ_(k) s_(M−1)=1 } }where θ is any suitable threshold for discriminating between phaseintervals exhibiting similar and dissimilar impairment characteristics(e.g., in one realization, d(σ_(i),σ_(j)) is small and σ_(i) and σ_(j)are to be grouped if d(σ_(i),σ_(j))≦θ). Note that use of a distancemeasure d(σ_(i),σ_(j)) such as the above-described sum-of-squares setdifference calculation is merely illustrative and persons of ordinaryskill in the art will appreciate a wide variety of suitablediscrimination functions.

In some realizations, the threshold value, θ, employed may bepredetermined (e.g., empirically), while in others, the threshold valuemay be computed based on observed sets of estimates. In one suchrealization, a threshold may be established based on observed distancemeasures between the sets of amplitude estimates. For example, one suchrealization:

$\theta = {\alpha\mspace{14mu}{\min\limits_{i,j}\left( {d\left( {\sigma_{i},\sigma_{j}} \right)} \right)}}$where α is selected to baseline the threshold off of a minimum distancebetween the sets of amplitude estimates. In one realization α=3/2.

While the above illustrated pseudocode groups a given phase intervalwith the first characteristic group for which a distance measure isbelow a threshold, it has been observed that such an implementation maynot group a particular phase interval with those that best match itsimpairment characteristics. Accordingly, an improved realization (below)illustrates a sequence of operations that may be implemented in acommunication device (e.g., in software or firmware) for defining a setof characteristic groups and associating individual phase intervals withthe characteristic groups that better corresponds to observed impairmentcharacteristics.

Initial step: M=1 γ₀={σ₀} σ′₀=σ₀ s₀=1 General step: for k=1 to 23 {MinDistance = d(σ′₀,σ_(k)) MinIndex = 0 for m=1 to M−1 { distance =d(σ′_(m),σ_(k)) if (distance < MinDistance) { MinDistance = distanceMinIndex = m } } if (MinDistance < θ) {γ_(MinIndex)=γ_(MinIndex)∪{σ_(k)} s_(MinIndex)=s_(MinIndex)+1 } else {M=M+1 γ_(M−1)={σ_(k)} σ′_(M−1)=σ_(k) s_(M−1)=1 } }where each set of amplitude estimates, σ_(k), for a particular phaseinterval is added to a characteristic group to which it bestcorresponds, γ_(MinIndex), if the distance measure between that set ofamplitude estimates and the characteristic group is less than athreshold. Otherwise, a new group is defined.

While a variety of suitable implementations will be appreciated bypersons of ordinary skill in the art based on the above descriptions andpseudocode, the flow chart of FIG. 4 illustrates one suitable sequenceof operations. Initially, amplitude estimates for one of the 24 phaseintervals are treated (402) as representatives of a first characteristicgroup. Typically, estimates for phase interval 1 are assigned to thefirst characteristic group, although the particular phase intervalassigned is arbitrary. In general, phase interval 1 may be subject toRBS, padding or no periodic impairment at all. Next, amplitude estimatesassociated with another phase interval (typically, phase interval 2) areevaluated against then current characteristic groups. In theillustrative realization of FIG. 4, evaluation includes calculating(406) a set difference measure (such as described above) betweenamplitude estimates for the current phase interval (e.g., phase interval2) and representatives of each characteristic group (e.g., group 1characterized by amplitude estimates of phase interval 1). Based oncomparison with each of the characteristic groups, a best matchingcharacteristic group is identified. If the set difference measure meetsa match criterion (e.g., if the set difference measure is below athreshold value), then the current phase interval may be added (408) tothe matching characteristic group. If not, a new characteristic group isdefined (410) using amplitude estimates of the current phase interval asrepresentative thereof.

Focusing on an exemplary realization, assignment of a phase interval toa characteristic group may be based on use of a distance calculationthat focuses on a representative subset of amplitude estimates. Forexample, in some realizations, estimates of symbols corresponding toUchords four and five are employed. In one such realization, a setdifference calculation is performed during a first pass through loop404, comparing amplitude estimates σ₂ obtained in the second timingphase with a first group γ₁ characterized by amplitude estimates σ′₁obtained in the first timing phase, and can be represented as follows:

${d\left( {\sigma_{2},\sigma_{1}^{\prime}} \right)} = {{\sum\limits_{l = {- 79}}^{- 48}\;\left( {A_{l,2} - A_{l,1}^{\prime}} \right)^{2\;}} + {\sum\limits_{l = 48}^{79}\;\left( {A_{l,2} - A_{l,1}^{\prime}} \right)^{2}}}$Later passes through loop 404 may include comparisons with largernumbers of then-defined characteristic groups.

The quality of amplitude estimates used to characterize individualgroups can be improved by combining contributions from the various phaseintervals that are assigned to the characteristic group. For example, ina characteristic group that includes two or more timing intervals, theset of amplitude estimates corresponding to the same codeword may beaveraged or otherwise combined (e.g., using any suitable computationalmethod) for each of the corresponding phase intervals. In anillustrative realization, an averaged value A′_(i,m) for the i^(th)amplitude estimate characteristic of the m^(th) group may be calculatedas follows:

for i=−127 to 127 (each amplitude estimate) { for m=0 to M−1 (eachgroup) { A′_(i,m)=0 for k=0 to 23 (each phase) { if (σ_(k)εγ_(m)) {A′_(i,m)=A′_(i,m)+A_(i,k) } } A′_(i,m)=A′_(i,m)/s_(m) } }where σ′_(m)={A′_(i,m);−127≦i≦127}, 0≦m≦M−1. Persons of ordinary skillin the art will appreciate that the above pseudocode is merelyillustrative and that a particular implementation may employ similartechniques at any of a variety of points in a computation. For example,while some realizations may average amplitude estimates associated witha characteristic group after assignment of phase intervals tocharacteristic groups, others incrementally refine (see 409, FIG. 4) arepresentative set σ′_(m) of amplitude estimates for each characteristicgroup using amplitude estimates from each assigned phase interval.Assignment of Constellation Points

Based on a grouping of phase intervals, such as the exemplary setdifference measure based grouping described above, a communicationsdevice operating in accordance with some embodiments of the presentinvention assigns constellation points based on the characteristics ofgrouped phases. For example, in some realizations, constellation pointsare assigned for each of several distinct constellation indices byselecting, for each such constellation index, successive candidate nextconstellation points that, based on symbol estimates for the one or morecharacteristic sets corresponding to the constellation index, satisfy adistance metric with respect to a last assigned constellation point forthe constellation index. From such a set of candidates, successivelowest power candidates are assigned as next constellation points inrespective constellations.

As before, realizations of the present invention may be betterunderstood in the context of an illustrative embodiment in accordancewith Recommendation V.90. Also as before, illustrative V.90 embodimentsare not meant to be limiting. To the contrary, based thereon, persons ofordinary skill in the art will appreciate a variety of suitablerealizations including those suitable for operation in the context ofother standards, future standards and non-standard communicationfacilities or protocols.

Similarly, the preceding description identifies a particularlyadvantageous organization for an impairment compensation sequence(sometimes encoded as a Digital Impairment Learning (DIL) sequence inaccordance with Recommendation V.90) and related techniques for groupingphase intervals based on correspondence of apparent aggregateimpairments. While grouping of phase intervals based on estimates ofreceived symbols corresponding to a 24 phase DIL sequence withcharacteristics such as described above is preferable, other methods ofgrouping may be employed as a precursor to the assignment ofconstellation points now described. For example, in one realizationgrouping is based on a 6 phase view of received sequences such thatthere is a one-to-one correspondence between phase intervals andconstellation indices. These and other variations will be appreciated bypersons of ordinary skill in the art based the description that follows.

In view of the foregoing, an illustrative V.90-oriented embodiment isnow described. Recommendation V.90 provides for six sets ofconstellation points, one for each of six timing instants (orconstellation indices) from 0 to 5. As described above, one particularlyadvantageous view of a DIL sequence is as a 24-phase symbol sequence,wherein a variety of potential impairments are known to be periodic atleast in 24 phase intervals (if not 6 or 12 phase intervals). In such anillustrative framework, a k^(th) constellation index corresponds to fourphase intervals k, k+6, k+12 and k+18. Accordingly, in realizations thatemploy a 24-phase view of symbol sequences, group associations for eachof the corresponding four phase intervals may be employed in theassignment of successive constellation points for a given constellationindex. Of course, in general, actual groupings are dependent on theparticular impairment characteristics of a communication channel.Accordingly, based on the particular impairments active in particulartiming phases of a particular communications channel, the four phaseintervals corresponding to a particular constellation index may beassociated with 1, 2, 3 or 4 groups.

In a simplified realization, two general cases need to be considered. Inthe first case, each of the phase intervals corresponding to aconstellation index is associated with a same characteristic group. Inmathematical terms, each of the phase intervals is associated with setof amplitude estimates characteristic of group γ_(m), i.e.,σ_(k)εγ_(m),σ_(k+6)εγ_(m),σ_(k+12)εγ_(m), and σ_(k+18)εγ_(m) for some m.In this case, the set of symbol estimates σ′_(m)={A′_(i,m);−127≦i≦127}can be used for selection of constellation points as follows: Let i_(l)be the smallest positive value of i such thatA′_(i,m)−A′_(−i,m)≧d_(min). For r≧2, let i_(r) be the smallest positivevalue of i such that A′_(i,m)−A′_(i) _(r−1) _(,m)≧d_(min) and A′_(−i)_(r−1) _(,m)−A′_(−i,m)≧d_(min). Continue this process for r=3,4, . . .as long as the constellation power (e.g., as defined in Clause 8.5.2 ofRecommendation V.90) does not exceed the maximum average power (P_(max))or until all the points in the set σ′_(m) (i.e., points corresponding to0≦i≦127) have been exhausted. The resulting set {i₁,i₂, . . . ,i_(r)}defines the constellation for constellation index k.

In the second case, the corresponding phase intervals are not allassociated with the same characteristic group. Instead, the phaseintervals may be associated with two, three or four characteristicgroups. For example, in the case of σ_(k)εγ_(m) ₁ , σ_(k+6)εγ_(m) ₂ ,σ_(k+12)εγ_(m) ₃ , and σ_(k+18)εγ_(m) ₄ where m₁, m₂, m₃, m₄ are not allequal, the sets of symbol estimates σ′_(m) ₁ , σ′_(m) ₂ ,σ′_(m) ₃ , andσ′_(m) ₄ are used as follows for selection of constellation points forconstellation index k: Let i₁ be the smallest positive value of i forwhich symbol estimates A′_(i,m) _(t) −A′_(−i,m) _(t) ≧d_(min) for everylε{1,2,3,4}. For r≧2, let i_(r) be the smallest positive value of i suchthat: min{(A′_(i,m) _(t) −A′_(i) _(r−1) _(,m) _(t) ),(A′_(−i) _(r−1)_(,m) _(t) −A′_(−i,m) _(t) }≧d_(min) for every lε{1,2,3,4}. Continuethis process for r=3,4, . . . as long as the constellation power doesnot exceed P_(max) or until all the points in the set corresponding to0≦i≦127 have been exhausted. The resulting set {(i₁,i₂, . . . ,i_(r)}defines the constellation for constellation index k.

Note that the final constellation is typically subject to additionalmanipulation that is somewhat independent of the techniques describedherein. In particular, legal regulations prohibit modems fromtransmitting at a power level that is greater than a specified maximum.This restriction sometimes leads to creation of a constellation forwhich addition of an additional point would exceed the maximum power,but such that using the derived set of points fails to use all of thepower available. In that instance the distance between the points in theresulting set can be increased in order to improve performance.Therefore, in practice an additional iteration can be performed on theset of constellation points obtained by following the above procedure.This iteration can be applied in addition to the steps described above.

Building on the above, some additional realizations are notable. Forexample, FIG. 5 illustrates a variation in which constellation pointsare assigned to constellations for each of 6 constellation indices in amanner that advantageously utilizes overall constellation power (i.e.,power collectively employed by a statistical distribution of informationtransmitted in phase intervals corresponding to each of theconstellation indices) to maximize information capacity. As before, aninitial point is selected for each of 6 constellations. In particular, aminimal Ucode is selected (501) such that, for each corresponding group(e.g., in an exemplary embodiment, the 1, 2, 3 or 4 groups associatedwith the four phase intervals corresponding to a given constellationindex), the difference between amplitude estimates for positive andnegative receptions of the Ucode is at least d_(min). Generally, thed_(min) parameter relates to an estimated signal-to-noise ratio on thetelephone line and determines the minimum spacing between constellationpoints consistent with a given level of performance. Additionally, legalregulations prohibit modems from transmitting at certain power levels.Recommendation V.90 defines this restriction, which is hereinafterreferred to as maximum power level, P_(max).

Note that in the Ucode set defined by Table 1 of Recommendation V.90,Ucodes are organized in order of increasing power. Accordingly, in anillustrative V.90 realization, a minimal Ucode is a lowest number Ucodethat meets the d_(min) criterion. For each of the 6 constellations sucha minimal Ucode is identified and added (502) as a first constellationpoint. Persons of ordinary skill in the art will appreciate suitableinterpretations for other coding schemes.

Successive constellation points are added to the 6 constellations asfollows. For each of the K constellation indices, a minimal candidateUcode is identified based on evaluation of a minimum spacing criterionin the context of amplitude estimates from the characteristic group (orgroups) corresponding thereto. In an exemplary realization, the minimumspacing criterion is based on the difference between a group-specificamplitude estimate and the Ucode last added to a current constellationexceeding d_(min). Then, a minimal one of the 6 minimal candidates isselected for addition to its corresponding constellation.

For example, assume that based on an evaluation (503) of the d_(min)criterion in the context of two characteristic groups γ₁ and γ₂ ofamplitude estimates associated with phase intervals 4, 10, 16, and 22corresponding to a 4^(th) constellation index, Ucode₂₂ is the minimalUcode for which estimates from both groups exceed the Ucode last addedto constellation 4 by at least d_(min). Further assume that thesimilarly calculated (503) minimal candidates for the 0^(th), 1^(st),2^(nd), 3^(rd) and 5^(th) constellation indices are Ucode₂₃, Ucode₂₄,Ucode₂₄, Ucode₂₃ and Ucode₂₄, respectively based on the aggregateimpairments observed in each of the phase intervals correspondingthereto (i.e., based comparison of the amplitude estimates for thecorresponding characteristic groups with respective last addedconstellation points). Based on the foregoing, Ucode₂₂ is selected (505)as the minimal one of the candidate Ucodes and is added (504) to thecorresponding constellation (i.e., constellation 4). A next candidate iscalculated (503) for the 4^(th) constellation index and a minimal one ofthe then current candidates is again selected for addition to itscorresponding constellation. For example, assuming that the nextcandidate for the 4^(th) constellation index is Ucode₂₄, a minimalcandidate (Ucode₂₃) is added to constellation 0. The process continuesuntil a selected candidate would, if added, cause overall constellationpower to exceed a maximum level, e.g., P_(max).

While the above description has assumed that all 6 constellation indicesare distinct, this need not be the case. Indeed, performance advantagesmay be achieved if constellation assignment calculations are notduplicated for indistinct indices. For example, based on the descriptionherein, persons of ordinary skill in the art will appreciate that if theset of characteristic groups associated with corresponding phaseintervals of two or more constellation indices are the same (i.e., thetwo or more constellation indices are indistinct), then selectionsperformed for one constellation index may be used in each of the others.

Resulting constellations may be transmitted to a remote communicationsdevice, e.g., to a remove V.90 server modem, using any suitablemechanism. For example, after an analog client modem operating inaccordance with an embodiment of the present invention receives a DILsequence, groups phases and assigns constellation points as describedabove, it may transmit an encoding of the resulting constellations backto a digital server modem. In one such realization, at least theassignment of constellation points is performed during the Phase 4—FinalTraining period defined by Recommendation V.90. Constellation parametertransfer protocols and mechanisms such as that defined by RecommendationV.90 are well known and realizations in accordance with the presentinvention may use any transfer mechanism suitable for the communicationsdevices and/or communications channels employed.

Exemplary Communication Systems and Device Embodiments

A typical communications system in accordance with the present inventionincludes a receiver (typically including an equalizer) to receive animpairment compensation sequence such as described above. Typically,such a receiver is provided as part of a communications device such asan analog V.90 modem, although other realizations will be appreciated bypersons of ordinary skill in the art based on the description herein. Insome realizations, characteristic groups are determined and impairmentsensitive selection of constellation points is performed based on thereceived impairment compensation sequence. In general, suitableimpairment compensation sequences are selected in accordance with theparticular signal processing structures employed by the receiver. Forexample, some of the description above emphasized impairmentcompensation sequences suitable for a receiver employing apartial-response IV equalizer (PRIV) or partial-response V equalizer(PRV). While not limited thereto, suitable realizations may beunderstood in the context of particular communications system and deviceconfigurations (including modems conforming to Recommendation V.90)employing a partial response class V (PRV) equalizer structure such asdescribed in greater detail in

U.S. patent application Ser. No. 09/249,990, filed on Feb. 13, 1999,entitled “Efficient Reduced State Maximum Likelihood SequenceEstimator,” now U.S. Pat. No. 6,618,451.

Referring illustratively to FIG. 6, an exemplary V.90 modemimplementation employs a reduced state maximum likelihood sequenceestimator and a partial response class V equalizer. A brief descriptionof the illustrated modem will provide a context for better understandingsome device embodiments in accordance with the present invention. Adetailed discussion of the operation of the exemplary modem is omittedsince modem operation in conformance with Recommendation V.90 is knownthe art. More detailed information may be found in theabove-incorporated U.S. Patent Application and in Recommendation V.90.In an illustrative embodiment, partial response equalizer 619 isimplemented in software that may be stored on computer readable mediathat can be executed on a suitable processor. Those of skill in the artwill appreciate that the teachings herein may be applied to a variety ofmodem and communication device implementations (see, for example, FIG.7) including those employing a programmable digital signal processor(e.g., processor 702) and/or specialized logic.

The illustrated modem includes both transmitter 601 and receiver 603portions. In general, DIL descriptor information is supplied usingtransmitter portion 601, while a corresponding DIL sequence is receivedusing receiver portion 603. Constellations selected as described hereinare communicated using transmitter portion 601. Transmitter data module605 supplies a digital bit stream to encoder 607. Transmitter datamodule 605 may generate such digital data locally in the case of startupor training (including DIL descriptor supply) or may fetch or receivedata from an external data source or application program (not shown) indata mode. Transmitter data module 605 passes the data to the encoder607, which in turn converts the input bit stream into a sequence ofsymbols that are then provided to modulator 609. Modulator 609 performsappropriate sampling and filtering operations and provides its output toshaping and preemphasis filter 611, which in turn providessquare-root-of raised cosine shaping as well as preemphasis filtering asspecified by Recommendation V.90. Note that during certain phases ofmodem operation, including supply of a DIL descriptor, spectral shapingis disabled. The resultant modulated, encoded signal is supplied to acommunications channel (not shown) by digital-to-analog converter 613.

Receiver portion 603 of the illustrated modem receives the output fromthe transmitter (prior to the D/A) into receiver front end 615. Receiverfront end also receives a received signal 616 from the communicationschannel. Receiver front end 615 performs operations such asanalog-to-digital conversion on the received signal, various filteringand echo-canceling operations and provides its output to demodulator617. Demodulator 617 includes partial response class V equalizer 619.Accordingly, DIL sequences organized as described above for PRVequalizers are suitable for supply to the illustrated modem andcharacteristic group determinations and impairment sensitive selectionof constellation points based on the equalized DIL sequences may beemployed. In the illustration of FIG. 6, demodulator 617 also includes asecond stage near-end echo canceller 620, which cancels the echo at theoutput of the equalizer and is intended to track slow variations of theecho signal. The output of the partial response equalizer is provided todecoder 621, and more specifically to reduced state maximum likelihoodsequence estimator 623 thereof.

In data mode, symbols decoded by maximum likelihood sequence estimator623 are split into sign and amplitude components and passed respectivelyto the spectral de-shaper 625 and modulus decoder 627. These modulesextract the data payload from the symbols that is later converted to abit stream by data assembler 629. Receive data module 631 descramblesthe bit stream and, in general, passes it to an application program (notshown).

For DIL operations described herein, amplitude estimates are, ingeneral, processed at the equalizer output although other points in thesignal flow of FIG. 6 may also be suitable. In particular, based on suchamplitude estimates, the illustrated modem assigns each phase of thereceived sequence to a characteristic group as described in greaterdetail above. Similarly, constellation points are selected for eachcharacteristic group of phases as described in greater detail above.Constellation point selections are transmitted to a remote modem (notshown) using transmitter portion 601 in accordance with the “Phase4—Final training” protocol of Recommendation V.90.

In general, techniques described herein support improved impairmentcompensation sequences, methods and signal processing configurations. Insome realizations, improved digital impairment learning in accordancewith Recommendation V.90 is provided. Based on the description herein,persons of ordinary skill in the art will appreciate a variety ofapplications of the underlying techniques and the breadth of theinvention. Without limitation thereto, a V.90 modem configurationprovides a useful example. Some of the exemplary embodiments have beendescribed in a largely software context to provide clarity to theinvention. While such software implementations of the invention arecertainly contemplated, the teachings disclosed herein may also be usedby persons of ordinary skill in the art to implement the presentinvention in a hardware or mixed hardware/software context withoutdeparting from the scope of the invention.

1. A method for selecting points for inclusion in a multipointconstellation, the method comprising: grouping phase intervals intogroups based on similarity of an aggregate impairment exhibited thereinand calculating a characteristic set of one or more symbol estimates ofone or more of the phase intervals for each of the groups; and assigningconstellation points for a current constellation index corresponding toa plurality of phase intervals, based on one or more characteristic setscorresponding thereto, wherein one or more characteristic sets includecontributions of symbol estimates from the phase intervals associatedwith one or more constellation indices other than the currentconstellation index.
 2. A method, as recited in claim 1, furthercomprising: performing the assigning collectively for each of J distinctconstellation indices, where J>O, wherein the assigning includes:selecting, for each of the J distinct constellation indices, successivecandidate next constellation points that, based on the symbol estimatesfor the one or more characteristic sets corresponding to the currentconstellation index, satisfy a distance metric with respect to a lastassigned constellation point for the current constellation index; andassigning successive lowest power ones of the candidate nextconstellation points to respective ones of the J distinct constellationindices.
 3. A method, as recited in claim 1, wherein each of the phaseintervals corresponding to the current constellation index is a memberof a same group; and wherein the assigning further includes selecting anext constellation point such that a distance metric between agroup-characteristic estimate thereof and a last selected constellationpoint for the current constellation index satisfies a minimum distancecriterion.
 4. A method as recited in claim 1, wherein at least two phaseintervals corresponding to the current constellation index are membersof different groups; and wherein the assigning further includesselecting a next constellation point such that a distance metric betweengroup-characteristic estimates thereof and a last selected constellationpoint for the constellation index satisfies a minimum distance criterionfor the at least two phase intervals.
 5. A method, as recited in claim1, wherein the current constellation index is a k^(th) one of sixconstellation indices, where k≧0; and wherein a k^(th) one of the phaseintervals, a (k+6)^(th) one of the phase intervals, a (k+12)^(th) one ofthe phase intervals and a (k+18)^(th) one of the phase intervals eachcorrespond to the constellation index.
 6. A method, as recited in claim1, wherein multiple phase intervals correspond to the currentconstellation index.
 7. A method, as recited in claim 1, wherein asingle phase interval corresponds to the current constellation index. 8.A method, as recited in claim 1, wherein the phase intervals numbertwenty-four; and wherein the current constellation index is one of sixconstellation indices.
 9. A method, as recited in claim 1, furthercomprising: performing the grouping based on a received impairmentcompensation sequence that places at least one instance of each symbolfrom a predetermined set of symbols in each of the phase intervals. 10.A method, as recited in claim 1, further comprising: communicating theconstellation points to a remote communications device.
 11. A method, asrecited in claim 1, wherein the symbol estimates include amplitudeestimates of pulse code modulation codewords.
 12. A method, as recitedin claim 1, wherein the distance metric includes a set differencemeasure based on respective amplitude estimates corresponding torepresentation groupings of pulse code modulation codewords.
 13. In acommunications system for communicating via a channel susceptible to oneor more potential impairments each periodic in an integer N samples of areceived signal, where N>1, a method for mapping constellation points toone or more constellations, the method comprising: receiving a sequenceof symbol estimates organized into N phases, a respective plurality ofthe phases corresponding to a particular one of J constellation indiceswhere J>0; grouping the N phases into a set of characteristic groupsaccording to aggregate effects of the periodic impairments, if any,present in the N phases and without a priori identification ofindividual forms of the periodic impairments present therein; and forthe particular one of J constellation indices, selecting theconstellation points based on one or more of the characteristic groups,the one or more of the characteristic groups being associated with therespective plurality of the phases.
 14. A method, as recited in claim13, wherein the selecting includes, for each of the J constellationindices, selecting successive candidate next constellation points that,based on the characteristic groups associated with the respectiveplurality of the phases, satisfy a distance metric with respect to alast assigned constellation point for the particular one of Jconstellation indices; and assigning successive lowest power ones of thecandidate next constellation points to respective constellation indices.15. A method, as recited in claim 13, wherein the selecting of theconstellation points for the particular one of J constellation indicesincludes: calculating, for each associated characteristic group, adistance metric between a constellation point last added to theparticular one of J constellation indices and estimates of a pluralityof next lowest power constellation points; and selecting for additionfor the particular one of J constellation indices, one of the nextlowest power constellation points for which the calculated distancemetric exceeds a minimum distance metric for each associatedcharacteristic group.
 16. A method, as recited in claim 13, wherein theselecting of the constellation points for the particular one of Jconstellation indices includes: for each associated one of thecharacteristic groups, finding a next lowest power constellation pointfor which a distance metric between an estimate of the next lowest powerconstellation point and a constellation point last added to theparticular one of J constellation indices exceeds a minimum distancemetric; and adding for the particular one of J constellation indices, ahighest power one of the next lowest power constellation pointsassociated with the characteristic groups.
 17. A method, as recited inclaim 13, wherein each of the N phases corresponding to a j^(th)constellation index is associated with a single characteristic groupwhere j≧0 and wherein selecting for a particular constellationcorresponding to the j^(th) constellation index includes selecting foraddition to the particular constellation, a next lowest powerconstellation point for which a distance metric between a constellationpoint last added to the particular constellation and an estimate of thenext lowest power constellation point exceeds a minimum distance metric.18. A method, as recited in claim 13, wherein N is
 24. 19. A method, asrecited in claim 13, wherein J is
 6. 20. A communication device forcommunicating, using one or more constellations, via a channelsusceptible to one or more potential impairments each periodic in aninteger N samples of a received signal, the communications devicecomprising: a receive path for receiving from the channel a sequence ofsymbols organized into N phase intervals, wherein a respective pluralityof the phase intervals correspond to a particular one of J constellationindices where J>0; and an impairment compensator coupled into thereceive path during a training mode to receive the sequence of symbolsand group the N phase intervals thereof into a set of characteristicgroups according to aggregate effects of the periodic impairments, ifany, the impairment compensator selecting, for the particular one of theJ constellation indices, constellation points based on one or more ofthe characteristic groups, the one or more of the characteristic groupsbeing associated with the respective plurality of the phase intervalscorresponding thereto.
 21. The communication device of claim 20 whereinthe one or more of the characteristic groups associated with therespective plurality of the phase intervals corresponding to the atleast one of the J constellation indices include contributions of symbolreceptions of the sequence of symbols in grouped phase intervalscorresponding to other constellation indices, such that selection ofconstellation points for the particular one of the J constellationindices is improved by symbol receptions from substantially all phaseintervals exhibiting similar aggregate effects of the periodicimpairments.
 22. The communication device of claim 20, furthercomprising: a transmit path, wherein the impairment compensator iscoupled to the transmit path to supply an encoding of the constellationpoints selected by the impairment compensator to a remote communicationsdevice.
 23. The communication device of claim 20, wherein for aparticular received sequence, respective phase intervals correspondingto two or more indistinct ones of the J constellation indices areidentically grouped; and distinct ones of the J constellation indicesnumber J.
 24. The communication device of claim 20, wherein N is 24 andJ is
 6. 25. An apparatus comprising: means for organizing a receivedsequence of symbol estimates into N phases where N is an integer greaterthan 1; means for grouping the N phases into a set of characteristicgroups according to correspondence of aggregate effects of periodicimpairments, if any, present in the N phases; and means for selectingconstellation points for a constellation index corresponding to aplurality of the N phases using one or more of the received symbolestimates characteristic of one or more of the set of characteristicgroups associated with the plurality of the N phases.
 26. The apparatusof claim 25 wherein the means for selecting constellation points usingone or more of the received symbol estimates characteristic of the oneor more of the set of characteristic groups associated with theplurality of the N phases includes: means for selecting candidate nextconstellation points for each of J distinct constellation indices, whereJ>0; and means for assigning successive lowest power ones of thecandidate next constellation points to respective constellations.
 27. Acomputer program stored on a computer readable medium comprising:instructions executable on at least one processor to at least partiallyimplement a communications device; and said instructions including animpairment compensation subset thereof executable to group N phases of asymbol sequence received by the communications device into a set ofcharacteristic groups according to correspondence of aggregate effectsof periodic impairments, if any, present in the N phases, where N is aninteger greater than 1, the impairment compensation subset ofinstructions selecting constellation points for a constellation indexcorresponding to a plurality of the N phases using one or more symbolestimates characteristic of the one or more characteristic groupsassociated with the plurality of the N phases.
 28. A computer programstored on a computer readable medium as in claim 27 wherein theinstructions are encoded by or transmitted in at least one computerreadable medium selected from the set of a disk, tape or other magnetic,optical, or electronic storage medium and a network, wireline, wirelessor other communications medium.
 29. The communication device of claim 20further comprising a partial response class V (PRV) equalizer coupled inthe receive path.
 30. The method as recited in claim 9 furthercomprising using a partial response class V (PRV) equalizer on thereceived impairment compensation sequence.
 31. The method of claim 13,wherein each of the characteristic groups exhibits a differentimpairment characteristic.
 32. The method of claim 13, wherein theselecting of the constellation points includes identifying a symbol codefor which symbol amplitude estimates from each of a plurality of thecharacteristic groups associated with the plurality of the phases exceeda symbol estimate associated with a last assigned constellation point.33. The method of claim 13, wherein the plurality of the phases aretiming phases, and each of the timing phases includes a symbolassociated with an amplitude level.
 34. The apparatus of claim 25,wherein each of the characteristic groups exhibits a differentimpairment characteristic.
 35. The apparatus of claim 25, wherein themeans for selecting constellation points includes means for identifyinga symbol code for which symbol amplitude estimates from each of aplurality of the characteristic groups associated with the plurality ofthe N phases exceed a symbol estimate associated with a last assignedconstellation point.
 36. The method of claim 13, wherein the pluralityof the phases are timing phases, and each of the timing phases includesa symbol associated with an amplitude level.